Question -
Answer -
Thegiven function is f (x) = cos (x2)
Thisfunction f is defined for every real number and f canbe written as the composition of two functions as,
f = g o h,where g (x) = cos x and h (x)= x2
Ithas to be first proved that g (x) = cos x and h (x)= x2 are continuous functions.
It isevident that g is defined for every real number.
Let c bea real number.
Then, g (c)= cos c
Therefore, g (x)= cos x is continuous function.
h (x)= x2
Clearly, h isdefined for every real number.
Let k bea real number, then h (k) = k2
Therefore, h isa continuous function.
It isknown that for real valued functions g and h,suchthat (g o h) is defined at c, if g iscontinuous at c and if f is continuousat g (c), then (f o g) iscontinuous at c.
Therefore, 
is a continuousfunction.